Constraining modified theories of gravity through the detection of one extremely large mass-ratio inspiral

TL;DR

This work tests modified gravity using extremely large mass-ratio inspirals (XMRIs) of brown dwarfs into Sgr A*, leveraging space-based GW detectors. By constructing XMRI waveforms in dynamical CS gravity via the Analytic Kludge/ppE framework and applying fitting-factor, Fisher, and time-frequency Bayesian methods, the study quantifies how well the CS parameter $\zeta$ and source properties can be inferred. The results show that high-spin, high-eccentricity XMRIs near the MBH yield the strongest CS constraints, with $\log_{10}\zeta$ bounds ranging from approximately $-1$ to below $-4$ depending on evolution time and orbital parameters; Bayesian analyses demonstrate that most intrinsic parameters can be recovered within $1\sigma$, and $\zeta$ can be constrained more tightly for favorable sources. Overall, XMRIs provide a promising, complementary test of GR in the strong-field regime, capable of tightening Solar System bounds by several orders of magnitude and informing our understanding of gravity near massive black holes.

Abstract

Extremely large mass-ratio inspirals (XMRIs), formed by brown dwarfs inspiraling into a massive black hole, emit gravitational waves (GWs) that fall within the detection band of future space-borne detectors such as LISA, TianQin, and Taiji. Their detection will measure the astrophysical properties of the MBH in the center of our galaxy (SgrA$^\ast$) with unprecedented accuracy and provide a unique probe of gravity in the strong field regime. Here, we estimate the benefit of using the GWs from XMRIs to constrain the Chern-Simons theory. Our results show that XMRI signals radiated from the late stages of the evolution are particularly sensitive to differences between Chern-Simons theory and general relativity. For low-eccentricity sources, XMRIs can put bounds on the Chern-Simons parameter $ζ$ at the level of $10^{-1}$ to an accuracy of $10^{-3}$. For high-eccentricity sources, XMRIs can put bounds on the parameter $ζ$ at the level of $10^{-1}$ to an accuracy of $10^{-6}$. Furthermore, using the time-frequency MCMC method, we obtain the posterior distribution of XMRIs in the Chern-Simons theory. Our results show that almost all the parameters can be recovered within $1σ$ confidence interval. For most of the intrinsic parameters, the estimation accuracy reaches $10^{-3}$. For the brown dwarf mass, the estimation accuracy reaches $10^{-1}$, while for $ζ$, the estimation accuracy reaches $Δ\log_{10}ζ=0.08$ for high eccentricity sources and 1.27 for low eccentricity sources.

Figures (6)

• Figure 1: The overlap results for s1, s2 and s3 from Table \ref{['tabel:sources']}, where $p$ is given in units of mass $M$. The red, blue, orange, and green dash-dotted lines correspond to $T=0.5, 1.0, 2.0, 5.0$ years, respectively. The gray dashed lines correspond to the threshold value that can be distinguished.
• Figure 2: The overlap results for sources s4, s5, and s6, respectively, where $p$ is given in units of mass $M$. We use the same convention as in Fig. \ref{['fig:overlap1']}.
• Figure 3: The parameter estimation accuracy results of $\zeta$ for s1, s2 and s3, respectively, where the color indicates the estimation accuracy $\log_{10}\Delta\zeta$, the x-axis represents the values of $\log_{10}\zeta$, and the y-axis represents the evolution time for different sources, $p$ is given in units of mass $M$.
• Figure 4: The parameter estimation accuracy results of $\zeta$ for s4, s5 and s6, respectively, where $p$ is given in units of mass $M$. The same convention as in Fig.\ref{['fig:ParaEsti']}.
• Figure 5: Parameter estimation results using the time-frequency MCMC method for an XMRI with parameters as s1. Units: $M\,[M_\odot]$, $\mu\,[M_\odot]$, $\theta_K$ [rad], $\phi_K$ [rad], $\theta_S$ [rad], $\phi_S$ [rad], $\lambda$ [rad], $D$ [kpc], $p_0\,[M]$, $\phi_0$ [rad], $\gamma_0$ [rad], $\alpha_0$ [rad].